A mass of 0.12 kg is attached to a spring and set into oscillation on a horizont

Question

A mass of 0.12 kg is attached to a spring and set into oscillation on a horizontal frictionless surface. The simple harmonic motion of the mass is described by x(t) = (0.20 m)cos[(16 rad/s)t]. Determine the following.

(a) amplitude of oscillation for the oscillating mass

(b) force constant for the spring

(c) position of the mass after it has been oscillating for one half a period

(d) position of the mass one-third of a period after it has been released

(e) time it takes the mass to get to the position x = 0.10 m after it has been released

Explanation / Answer

here,

x(t) = ( 0.2 m) * cos(16 rad/s * t)

compairing with , x(t) = A * cos(w * t)

a)

the amplitude of the oscillating mass is 0.2 m

b)

angular frequency ,w = 16 rad/s

w = sqrt(k/m)

16 = sqrt(k/0.12)

k = 30.72 N/m

c)

Time period , T = 2 * pi /w

when

T = 2 * pi /(16)

T = 0.3925 s

at t = T/2 = 0.196 s

x(t) = 0.2 * cos( 16 * 0.196)

x(t) = - 0.2 m

d)

t = T/3 = 0.1308 s

x(t) = 0.2 * cos( 16 * 0.1308)

x(t) = - 0.1 m

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